CoqParam

CoqParam is the starting point of an implementation of a generator of
"theorems for free" in Coq, based on parametricity theory. For the
moment, it is made up with a tactic and a vernacular command that, given
a closed Coq term and its type, compute:

the parametricity relation generated by the type;

a proof that the term satisfies the parametricity relation.

It is a new way to prove some theorems in Coq, like commutation
theorems.

This is a prototype, and lots of things remain to do! In particular, it
would be nice to be able to automatically instantiate the free theorems
with the right parametricity relations to automatically solve Coq goals.

It is mainly developed
by Chantal
Keller at École Polytechnique and INRIA Saclay-Île-de-France
and Marc Lasson at
École Normale Supérieure de Lyon.